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Operati A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X- the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p - the probability that a diseas + test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results. Functio (a) Derive the maximum likelihood estimator of A fp. Symbol If n- 25 and x- 3, what is the estimate? Greek Hele (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n = 25 and x = 3, what is the mle of the probability (1 - p) that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.)

Operati A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X- the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p - the probability that a diseas + test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results. Functio (a) Derive the maximum likelihood estimator of A fp. Symbol If n- 25 and x- 3, what is the estimate? Greek Hele (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n = 25 and x = 3, what is the mle of the probability (1 - p) that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a diseas Operatic | test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results. Function (a) Derive the maximum likelihood estimator of p. Symbol= p =|| Relation Sets Trig If n = 25 and x = 3, what is the estimate? p = Greek O Help (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n = 25 and x = 3, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.) +
Transcribed Image Text:A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a diseas Operatic | test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results. Function (a) Derive the maximum likelihood estimator of p. Symbol= p =|| Relation Sets Trig If n = 25 and x = 3, what is the estimate? p = Greek O Help (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n = 25 and x = 3, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.) +
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